If the domain of `y=f(x)i s[-3,2],` then find the domain of `g(x)=f(|[x]|),w h e re \ [.]` denotes the greatest integer function.

Answer

[-2, 3)

Explanation

Here, `f(x)` is defined for `x in [-3,2].`
For `g(x)=f(|[x]|)` to be defined, we must have
`-3 le |[x]| le 2`
or `0le |[x]| le 2 " " ["As" |x| ge 0 " for all " x]`
or ` -2 le [x] le 2 " " ["As " |x| le a implies-a le x le a]`
or `-2 le x lt 3 " " ` [By the definition of greatest integral function]
Hence, domain of `g(x)` is `[-2,3)`.